Multiplying Algebraic Fractions

Imagine you wanted to multiply ab and cd.

How to Multiply Algebraic Fractions

To multiply algebraic fractions, use the rule:

A Real Example of How to Multiply Algebraic Fractions

An Example Question

Multiply the algebraic fractions below.

Step 1

Compare the fractions you are multiplying with the rule shown above.

By comparing, we see that a = x, b = 2, c = y, d = 3.

Step 2

Use the rule, with a = x, b = 2, c = y, d = 3:

Step 3

Calculate the terms in the rule. Where we have written two numbers or letters in brackets together, multiply them together:

(x)(y) = x × y = xy

(2)(3) = 2 × 3 = 6

We have multiplied x2 and y3 together:

Another Real Example of How to Multiply Algebraic Fractions

The slider below shows a real example of how to multiply algebraic fractions.

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Understanding the Rule

Multiplying fractions requires:

• multiplying the numerators together to form the numerator of the product...

• ... and multiplying the denominators together to form the denominator of the product:

This gives the rule:

The letters written next to each other denotes that they are multiplying each other.

The rule works when the a, b, c and d are numbers, letters, terms or expressions.

Make sure you can:

Cancelling Terms

When the numerator of one fraction equals the denominator of the other fraction, they cancel each other out:

This is how to simplify algebraic fractions.